design of automobile powertrain

the resistances that a automobile engine has to overcome while moving the vehicle are :

rolling resistance : the frictional resistance between the wheels and ground.

gradient resistance : the resistance that the vehicle experiences while climbing a flyover.

aerodynamic drag : the wind resistance.

now if we were to design a vehicle such that it would only move on level ground and never climb flyovers, then would it be safe not to consider the gradient resistance, while doing the design calculations for its engine , (like maximum torque and horse power ?) ?

When the vehicle moves on a level road, the total resistance is equal to rolling resistance + air resistance. Whether it is safe or not depends on what is your objective. If you are doing these calculations for a vehicle that is to be manufactured later on then you must include gradient resistance. Otherwise if you are doing some theoretical work only then you can make an assumption and neglect gradient resistance.

now supposing that the gradient resistance has not been considered in the calculations and an engine/motor has been selected based on the result of the calculation. now when the vehicle with this prime mover is made to climb a flyover or an uphill slope , then what would happen ? will the engine stall ? even if it does at what point would it stall ? at the entrance or at some point in the middle ?

now supposing that the gradient resistance has not been considered in the calculations and an engine/motor has been selected based on the result of the calculation. now when the vehicle with this prime mover is made to climb a flyover or an uphill slope , then what would happen ? will the engine stall ? even if it does at what point would it stall ? at the entrance or at some point in the middle ?

When the vehicle travels uphill, a component of its weight works in a direction opposite to its motion. If some energy is not supplied to overcome this backward force, then the vehicle would slow down, stall and roll backwards. This is the reason why it is necessary to include gradient resistance.

Chances are quite high that the engine will stall. Now where it will stall, it is not possible for me to predict as it will vary with different situations.